Mil. W. M. Buchanan's Tluory of the Reaction Water- Wheel. 121 



about 12 cubic feet of water per minute, under a head of 10 feet. The 

 area of the orifices was determined with the utmost precision ; and provi- 

 sion being made for measuring the water discharged within the five 

 thousandth part of a cubic foot in 2 minutes, the velocity of emission 

 could be calculated with great exactness from the relation, 

 Volume of water, = vcloci rf efflui 

 Area of orifices, 



To determine the corresponding reaction, one arm of a friction-brake 

 applied upon the vertical spindle of the machine, was loaded with a weight 

 known to bo considerably less than the pressure to be measured, and the 

 other was attached to a delicate dynamometer, which indicated the addi- 

 tional weight necessary to balance the reaction, and keep the machine at 

 rest. It would be tedious to describe the precautions adopted to secure 

 accuracy ; but it may be remarked, that the effect of the friction of the 

 journals, which is the most obvious source of error, was eliminated, by 

 causing the arms of the brake, and consequently the machine, to oscillate 

 slowly through a small arc, and taking the mean of the tension on the 

 dynamometer when the motion was with, and opposed to the direction 

 of the jets. The experiments were, besides, only accepted when satis- 

 factory : in every instance when a doubt arose, the experiment was can- 

 celled. The mean of the recorded results was subsequently calculated 

 by Legendre's method of Least Squares, and stood thus : The velocity 

 of efflux determined from the volume of water discharged was found to 

 be that due to 0*85682 of the mean actual head of 10 feet, taken as 

 unity ; and the hydraulic reaction referred to a column of water having 

 the sum of the areas of the orifices as a base, was 1*80832 of the samo 

 actual mean head. We have therefore the general ratio of comparison, 

 •85682 II 1 



1-80832 H " 21105 

 that is, the head duo to the velocity of efflux at the orifices being iss 1, 

 tho measure of the reaction referred to the same unit = 2*1 105, which is 

 greater by ^^ H than the measure assigned by theory. 



This result, which at first view appears anomalous, is corroborated by 

 the experiments which have been made to determine tho hydraulic pres- 

 sure of isolated jets projected perpendicularly against a plane surface. 

 Newton (Principiay Bk. II.) demonstrated from elementary principles 

 that tho measure of tho impulse of tho jet is identical with that stated 

 by Bernouilli as the measure of the reaction ; and M. Poisson (Mechanics, 

 Bk. V.) arrives at the same conclusion by a different process of reasoning. 

 But on submitting the proposition to the test of experiment, it has been 

 found that the actual -result is uniformly in excess of that assigned by 

 calculation ; and moreover, that the ratio varies with the head-pressure, 

 and also with the size of orifice. Thus in the experiments of M. Morosi, 



the ratio from difference of head alone varied from _- to ■ ; and 



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